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# Geometry || 29.03.2021

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Question 1

ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and angle ADC = 126°. BAC is equal to:

Question 2

ABC is an equilateral triangle in which D, E and F are the points on sides BC, AC and AB, respectively, such that AD ⊥ BC, BE ⊥ AC and CF ⊥ AB. Which of the following is true?

Question 3

In the figure, in ∆PQR, PT QR at T and PS is the bisector of QPR. If ∠PQR = 78o, and ∠TPS = 24o, then the measure of ∠PRQ is: Question 4

A is a point at a distance 26 cm from the centre O of a circle of radius 10 cm. AP and AQ are the tangents to the circle at the point of contacts P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ intersect AP at B and AQ at C, then the perimeter of ∆ABC is:

Question 5

Two circles of radii 7 cm and 9 cm intersect at the points A and B. If AB = 10 cm and the distance between the centers of the circles is x cm, then the value of x is:

Question 6 In the given figure, if OQ=QR, then the value of m is:

Question 7

In a quadrilateral ABCD, E is a point in the interior of the quadrilateral such that DE and CE are the bisectors of D and ∠C, respectively. If ∠B = 82° and ∠DEC = 80°, then ∠A =?

Question 8

In ∆ABC, O is the incentre and ∠BOC = 135°. The measure of ∠BAC is:

Question 9

In ABC, AB = c cm, AC = b cm and CB = a cm. If A = 2B, then which of the following is true?

Question 10

The distance between the centres of two circles of radius 4 cm and 2 cm is 10 cm. The length (in cm) of a transverse common tangent is:
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